Respuesta :
Answer:x= 36 y= 67 and z=77
Step-by-step explanation: we have to write the equations from the data give in the exercise, this means :
First of all, x,y and z correspònd to the first, second and third angles, respectively.
The sum of the measures of the angles of a triangle is 180
can be written as x+y+z=180
The sum of the measures of the second and third angles is four times the measure of the first angle.
It can be written by: x+y=4z
The third angle is 10 more than the second
It can be written as z=y+10
By solving the equations systems the above values can be determined.
x+y+z=180
x+y=4z
z=y+10
The required value of three angles first, second, and third angles, respectively x = 118, y = 26 and z = 36.
Given that,
The sum of two measure of the angle of a triangle is 180.
We have to find,
The measures of the three angles. Do not include degree symbol in your answer.
According to the question,
Let, The first angle be = x
the second angle be = y
And the third angle = z
Sum of measures of the angles of a triangle is 180.
Then,
x + y + z = 180
And The sum of the measures of the second and third angles is four times,
x + y = 4z
And The third angle is 10 more than the second,
It can be written as
z = y + 10
Solving the equation 2 and 3
x + y = 4 ( y + 10 )
x + y = 4y + 40
x = 40 + 3y
Put the value of x in the equation 1
x + y + z = 180
40 + 4y + z = 180
Substitute the value of z from equation 3
40 + 4y + y + 10 = 180
50 + 5y = 180
5y = 180 - 50
5y = 130
[tex]y = \frac{130}{5}[/tex]
y = 26
And
z = 10 + 26 = 36
Again x + 36 + 26 = 180
x = 180 - 62
x = 118
Hence, The required value of three angles x = 118, y = 26, z = 36.
For the more information about Triangle click the link given below.
https://brainly.com/question/2773823
